Linear Momentum Balance in Aerodynamic Thrust

The force generated by a jet engine on a static thrust stand can be determined using Newton's second law of motion, in which the time rate of change of the linear momentum of the system is equal to the sum of external forces acting on the system. For a fixed, nondeforming control volume with uniform and steady flow, the sum of the forces is equal to the net rate of linear momentum flow through each control surface. This Demonstration illustrates the effects of air density, intake velocity and pressure, and control surface areas on the resultant anchoring force () necessary to hold the jet engine stationary.

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The linear momentum balance for a nondeforming, stationary control volume is . Since the flow is steady, the momentum balance simplifies to , where is velocity, is the density of the fluid, represents the product of the component of velocity normal to the control surface, and is the differential area of the control surface. The velocity coming out of the turbine is determined using the continuity equation for an incompressible fluid, . The overall force balance takes into account the pressures at the inlet and the outlet. , where is the resultant force, is the intake pressure, and is fixed at 0 kPa for this Demonstration.